Laplace Transform of Integrals

So I know the laplace transform of an integral is the product of the laplace transorm of the functions inside the integral, such as Laplace{integral from 0 to t [tau*e^(t - tau) d tau = Laplace[t] * Laplace[e^t], ignoring the tau

what if I have Laplace{integral from 0 to t [t*e^(-tau) d tau], how do I break it down into 2 laplace functions? The answer is (1/s) * (1/(s + 1)^2), I don't get it. :/

Sorry, I don't know how to type an equation but hopefully you know what I mean. Any help is appreciated.